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3 years ago

How do I solve this?

Mathematics

1 answer:

Sindrei [870]3 years ago

5 0

Answer:

Set up the problem like a ratio by using fractions.

Step-by-step explanation:

For every 3oz it costs $10, and you're trying to find out the amount you can get for $15.

If you set up 3/10 = x/15, you can solve for x by multiplying 3 and 15 together, giving you 45. After that, you divide 45 by 10 and you will get the answer 4.5

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Find an equation of the sphere containing all surface points P = (x, y, z) such that the distance from P to A(−3, 6, 3) is "twic

Marina86 [1]

Answer:

Equation of Sphere = $x^{2}$ + $y^{2}$ + $z^{2}$ - 18x - 4/3y +10z + 142/3 = 0

Step-by-step explanation:

Data Given:

P = (x,y,z)

Distance from P to A (-3,6,3) = Twice the distance from P to B(6,2,-3)

Solution:

Find the equation of the sphere:

It is given that:

PA = 2PB

Squaring both sides:

$(PA)^{2} = (2PB)^{2}$

$(PA)^{2} = 4 (PB)^{2}$

$(x - (-3))^{2}$ + $(y - 6)^{2}$ + $(z-3)^{2}$ = 4 x $(x-6)^{2}$ + $(y-2)^{2}$ + $(z-(-3))^{2}$

Solving the above equation:

$(x + 3))^{2}$ + $(y - 6)^{2}$ + $(z-3)^{2}$ = 4 x { $(x-6)^{2}$ + $(y-2)^{2}$ + $(z + 3))^{2}$ }

$x^{2}$ + 9 + 6x + $y^{2}$ + 36 - 12y + $z^{2}$ + 9 - 6z = 4 { $x^{2}$ + 36 - 12x + $y^{2}$ + 4 - 4y + $z^{2}$ + 9 + 6z}

$x^{2}$ + 9 + 6x + $y^{2}$ + 36 - 12y + $z^{2}$ + 9 - 6z = 4 $x^{2}$ + 144 - 48x +4 $y^{2}$ + 16 - 16y + 4 $z^{2}$ + 36 + 24z

Putting the right hand side = 0 and solving the equation:

$x^{2}$ - 4 $x^{2}$ + $y^{2}$ - 4 $y^{2}$ + $z^{2}$ - 4 $z^{2}$ + 6x + 48x - 12y +16y -6z - 24z + 9 + 36 + 9 -144 - 16 - 36 = 0

-3 $x^{2}$ - 3 $y^{2}$ -3 $z^{2}$ + 54x + 4y -30z -142 = 0

Taking (-) common

- ( 3 $x^{2}$ + 3 $y^{2}$ + 3 $z^{2}$ - 54x - 4y +30z + 142) = 0

3 $x^{2}$ + 3 $y^{2}$ + 3 $z^{2}$ - 54x - 4y +30z + 142 = 0

dividing the whole equation by 3

$x^{2}$ + $y^{2}$ + $z^{2}$ - 54/3x - 4/3y +30/3z + 142/3 = 0

$x^{2}$ + $y^{2}$ + $z^{2}$ - 18x - 4/3y +10z + 142/3 = 0

7 0

3 years ago

A company has a policy of retiring company cars; this policy looks at number of miles driven, purpose of trips, style of car and

vredina [299]

Answer:

2.35%

Step-by-step explanation:

Mean number of months (M) = 39 months

Standard deviation (S) = 10 months

According to the 68-95-99.7 rule, 95% of the data is comprised within two standard deviations of the mean (39-20 to 39+20 months), while 99.7% of the data is comprised within two standard deviations of the mean (39-30 to 39+30 months).

Therefore, the percentage of cars still in service from 59 to 69 months is:

$P_{59\ to\ 69}=\frac{P_{9\ to\ 69}-P_{19\ to\ 59}}{2} \\P_{59\ to\ 69}=\frac{99.7-95}{2}\\P_{59\ to\ 69}=2.35\%$

The approximate percentage of cars that remain in service between 59 and 69 months is 2.35%.

8 0

3 years ago

In the diagram, lines AB , CD, and EF intersect at G

Ghella [55]

Answer:

D. 70°

Step-by-step explanation:

Given:

m<DGB = 35°

m<CGF = 75°

Required:

m<AGE

SOLUTION:

m<EGD = m<CGF (vertical angles are congruent)

m<EGD = 75°

m<AGE + m<EGD + m<DGB = 180° (angles on a straight line)

m<AGE + 75° + 35° = 180° (substitution)

m<AGE + 110° = 180°

Subtract 110 from each side of the equation

m<AGE = 180° - 110°

m<AGE = 70°

6 0

3 years ago

Use the identity (x+y)(x^2−xy+y^2)=x^3+y^3 to find the sum of two numbers if the product of the numbers is 28, the sum of the sq

lara31 [8.8K]

Step-by-step explanation:

We have xy = 28, x² + y² = 65 and x³ + y³ = 407.

Since (x + y)(x² - xy + y²) = x³ + y³,

x + y = (x³ + y³)/(x² + y² - xy)

= (407) / [(65) - (28)]

= 407 / 37

= 11.

Hence the sum of the numbers is 11.

4 0

3 years ago

Read 2 more answers

write an equation using ''x'' and then solve the equation. on the new year eve there were 7,580 tons of cargo loaded in the morn

vovikov84 [41]

Answer: 12,997 - 7,580 = x

x= 5417

Step-by-step explanation: 12,997 - 7580 = 5417

Hope this helps

8 0

4 years ago