5.8E: Exercises

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Practice Makes Perfect

Systems

Solve using systems.

1 pound of cereal A contains 7g of potassium and 2g of calcium. 1 pound of cereal B contains 5g of potassium and 3g of calcium. How many pounds of each cereal is needed to have a mixture of 17g of potassium and 8g of calcium?
1 pound of cereal A contains 5g of potassium and 2g of calcium. 1 pound of cereal B contains 6g of potassium and 1g of calcium. How many pounds of each cereal is needed to have a mixture of 21g of potassium and 7g of calcium?
1 pound of cereal A contains 2g of potassium and 2g of calcium. 1 pound of cereal B contains 3g of potassium and 1g of calcium. How many pounds of each cereal is needed to have a mixture of 10g of potassium and 6g of calcium?
1 pound of cereal A contains 6g of potassium and 1g of calcium. 1 pound of cereal B contains 3g of potassium and 3g of calcium. How many pounds of each cereal is needed to have a mixture of 57g of potassium and 22g of calcium?
1 pound of cereal A contains 5g of potassium and 2g of calcium. 1 pound of cereal B contains 3g of potassium and 3g of calcium. How many pounds of each cereal is needed to have a mixture of 8g of potassium and 5g of calcium?

Answer

We need 1 pounds of cereal A and 2 pounds of cereal B.
We need 3 pounds of cereal A and 1 pounds of cereal B.
We need 2 pounds of cereal A and 2 pounds of cereal B.
We need 7 pounds of cereal A and 5 pounds of cereal B.
We need 1 pounds of cereal A and 1 pounds of cereal B.

Rates

Solve

Suppose we have two people painting a house. Person A takes 2 hours to paint a house and Person B takes 1 hour to paint a house, how long will it take for them to paint a house working together?
Suppose we have two people painting a house. Person A takes 3 hours to paint a house and Person B takes 5 hours to paint a house, how long will it take for them to paint a house working together?
Suppose we have two people painting a house. Person A takes 4 hours to paint a house and Person B takes 5 hours to paint a house, how long will it take for them to paint a house working together?
Suppose we have two people painting a house. Person A takes 3 hours to paint a house and Person B takes 6 hours to paint a house, how long will it take for them to paint a house working together?
Suppose we have two people painting a house. Person A takes 1 hour to paint a house and Person B takes 5 hours to paint a house, how long will it take for them to paint a house working together?

Answer

It will take $\frac{2}{3}$ hours
It will take $\frac{15}{8}$ hours
It will take $\frac{20}{9}$ hours
It will take $2$ hours
It will take $\frac{5}{6}$ hours

Radicals

Landscaping Reed wants to have a square garden plot in his backyard. He has enough compost to cover an area of $75$ square feet. Use the formula $s=\sqrt{A}$ to find the length of each side of his garden. Round your answer to the nearest tenth of a foot.
Landscaping Vince wants to make a square patio in his yard. He has enough concrete to pave an area of $130$ square feet. Use the formula $s=\sqrt{A}$ to find the length of each side of his patio. Round your answer to the nearest tenth of a foot.
Gravity A hang glider dropped his cell phone from a height of $350$ feet. Use the formula $t=\frac{\sqrt{h}}{4}$ to find how many seconds it took for the cell phone to reach the ground.
Gravity A construction worker dropped a hammer while building the Grand Canyon skywalk, $4000$ feet above the Colorado River. Use the formula $t=\frac{\sqrt{h}}{4}$ to find how many seconds it took for the hammer to reach the river.
Accident investigation The skid marks for a car involved in an accident measured $216$ feet. Use the formula $s=\sqrt{24d}$ to find the speed of the car before the brakes were applied. Round your answer to the nearest tenth.
Accident investigation An accident investigator measured the skid marks of one of the vehicles involved in an accident. The length of the skid marks was $175$ feet. Use the formula $s=\sqrt{24d}$ to find the speed of the vehicle before the brakes were applied. Round your answer to the nearest tenth.

Answer

$8.7$ feet
$11.4$ feet
$4.7$ seconds
$15.8$ seconds
$72$ feet/second
$64.8$ feet/second

Maximum and minimum

An arrow is shot vertically upward from a platform $45$ feet high at a rate of $168$ ft/sec. Use the quadratic function $h(t)=-16 t^{2}+168 t+45$ find how long it will take the arrow to reach its maximum height, and then find the maximum height.
A stone is thrown vertically upward from a platform that is $20$ feet height at a rate of $160$ ft/sec. Use the quadratic function $h(t)=-16 t^{2}+160 t+20$ to find how long it will take the stone to reach its maximum height, and then find the maximum height.
A ball is thrown vertically upward from the ground with an initial velocity of $109$ ft/sec. Use the quadratic function $h(t)=-16 t^{2}+109 t+0$ to find how long it will take for the ball to reach its maximum height, and then find the maximum height.
A ball is thrown vertically upward from the ground with an initial velocity of $122$ ft/sec. Use the quadratic function $h(t)=-16 t^{2}+122 t+0$ to find how long it will take for the ball to reach its maximum height, and then find the maximum height.
A computer store owner estimates that by charging $x$ dollars each for a certain computer, he can sell $40 − x$ computers each week. The quadratic function $R(x)=-x^{2}+40 x$ is used to find the revenue, $R$, received when the selling price of a computer is $x$, Find the selling price that will give him the maximum revenue, and then find the amount of the maximum revenue.
A retailer who sells backpacks estimates that by selling them for $x$ dollars each, he will be able to sell $100 − x$ backpacks a month. The quadratic function $R(x)=-x^{2}+100 x$ is used to find the $R$, received when the selling price of a backpack is $x$. Find the selling price that will give him the maximum revenue, and then find the amount of the maximum revenue.

Answer

In $5.3$ sec the arrow will reach maximum height of $486$ ft.
In $5$ sec the stone will reach maximum height of $420$ ft.
In $3.4$ seconds the ball will reach its maximum height of $185.6$ feet.
In $3.8$ seconds the ball will reach its maximum height of $232.6$ feet.
$20$ computers will give the maximum of $$400$ in receipts.
$50$ backpacks will give the maximum of $$2500$ in receipts.