Gasoline costs 2.99 at the new gas station. if tom puts 8.5 gallons in his car what is the cost

Find the equation of the plane with the given description. contains the lines r1(t) = 2, 1, 0 + t, 2t, 4t and r2(t) = 2, 1, 0 +

Genrish500 [490]

The intersection point of the two lines is (2,1,0).
The respective direction vectors are
L1: <1,2,4>
L2: <4,1,15>
Since the normal vector of the required plane is perpendicular to both direction vectors, the normal vector of the plane is obtained by the cross product of L1 and L2.
i j k
1 2 4
4 1 15
=<30-4, 16-15, 1-8>
=<26, 1, -7>

We know that the plane must pass through (2,1,0), the equation of the plane is

26(x-2)+1(y-1)-7(z-0)=0
simplifying,
26x+y-7z=52+1+0=53
or
26x+y-7z=53

Check:
Put points on L1 in the plane
26(t+2)+(2t+1)-7(4t+0)=53 ok
For L2,
26(4t+2)+(t+1)-7(15t+0)=53 ok

8 0

3 years ago

Please help with 15, 17 and 19

Irina-Kira [14]

Given:

15. $\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)$

17. $\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)$

19. $2^{\log_2100}$

To find:

The values of the given logarithms by using the properties of logarithms.

Solution:

15. We have,

$\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)$

Using property of logarithms, we get

$\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)=1$ $[\because \log_aa=1]$

Therefore, the value of $\log_{\frac{1}{2}}\left(\dfrac{1}{2}\right)$ is 1.

17. We have,

$\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)$

Using properties of logarithms, we get

$\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)=-\log_{\frac{3}{4}}\left(\dfrac{3}{4}\right)$ $[\because \log_a\dfrac{m}{n}=-\log_a\dfrac{n}{m}]$

$\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)=-1$ $[\because \log_aa=1]$

Therefore, the value of $\log_{\frac{3}{4}}\left(\dfrac{4}{3}\right)$ is -1.

19. We have,

$2^{\log_2100}$

Using property of logarithms, we get

$2^{\log_2100}=100$ $[\because a^{\log_ax}=x]$

Therefore, the value of $2^{\log_2100}$ is 100.

6 0

3 years ago

Can someone figre this one out for me too plss with work shown and explanation NO LINKS AND NO DOING IT JUST FOR POINTS will giv

11111nata11111 [884]

Answer:

3 right and 1 up

Step-by-step explanation:

hope this helps!

8 0

3 years ago

Read 2 more answers

Mmmm! I love apple cider punch this time of year, and so do all my neighbors. My recipe calls for two quarts of apple cyder, thr

pickupchik [31]

Answer:

j

Step-by-step explanation:

8 0

3 years ago

Suppose legislation requiring the Fed to keep the inflation rate between 1.5% and 2.5% per year is passed by Congress. This law

Alborosie

Answer:

goal independence.

Step-by-step explanation:

The Fed is comprised of 12 regional federal reserve banks and its affairs are been directed by a board of governors. The characteristics fed has, granted to it by the congress, make they to remain very independent from the activities of the executive and legislative arms of the government. The Fed makes different policies and also implement them - which helps to ensure the employment of persons are up at all times and to create stability in prices and that of the interest rates.

4 0

3 years ago